Question

Mathematical Connections: The area of rectangle WXYZ is 115.5 square inches. What is the perimeter of triangle XYZ? (Round your answer to the nearest tenth if necessary!)

Answer 1

Given the area of the rectangle, WXYZ = 115.5 square inches

As shown in the figure: PQ = 4 in

so, the length of WX = 2 PQ = 2 x 4 = 8 in

The area of the rectangle =

$WX\cdot WZ=115.5$

So,

$WZ=\frac{115.5}{WX}=\frac{115.5}{8}=14.4375$

The length of XZ will be calculated using the Pythagorean theorem:

$\begin{gathered} XZ^2=WX^2+WZ^2=8^2+14.4375^2=272.44 \\ \\ XZ=\sqrt[]{272.44}=16.5058 \end{gathered}$

to the nearest tenth XZ = 16.5 inches

The perimeter of the triangle XYZ = XY + YZ + XZ

$\begin{gathered} XY=WZ=14.4375 \\ YZ=WX=8 \\ XZ=16.5 \\ \\ P=14.4375+8+16.5=38.943 \end{gathered}$

Rounding to the nearest tenth

so, the answer will be:

The perimeter of the triangle XYZ = 38.9 inches